Extreme Covering Systems
Jack Dalton and Ognian Trifonov
University of South Carolina
Department of Mathematics
Columbia, SC 29208
USA
Abstract:
We prove that if the least modulus of a distinct covering system is 4,
its largest modulus is at least 60; also, if the least modulus is 3,
the least common multiple of the moduli is at least 120; finally, if the
least modulus is 4, the least common multiple of the moduli is at least
360. The constants 60, 120, and 360 are best possible---they cannot be
replaced by larger constants.
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Received March 18 2022; revised versions received March 24 2022; August 18 2022.
Published in Journal of Integer Sequences,
October 27 2022.
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